The Question:

Why can't people with tattoos be buried in a Jewish
cemetery?

The Answer:

There is no such rule.

It is true that Jews are prohibited from getting tattoos under
Jewish law; the rule in question is in Leviticus 19:28.
With that said, violating this law does not disqualify one from burial
in a Jewish cemetery.

While this alleged rule was a central plot point in a 1996
episode of The Nanny, it is a complete myth, of
unknown origin. But you don't have to take our word for it. Here are
opinions by an Orthodox
rabbi and a
Conservative rabbi.